Applied Linear Algebra: The Decoupling Principle 2nd Edition by Lorenzo Sadun (PDF)

Description

Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I used this textbook when taking Columbia University’s APMA 4001: Principles of Applied Math, which is an intro-level graduate class in applied mathematics. As far as math textbooks go, this text is extremely clear and easy to read. It begins with a review of undergraduate linear algebra and proceeds to a rigorous treatment of eigenvalues and eigenvectors before ending with singular value decomposition and infinite-dimensional vector spaces. Sadun makes liberal use of examples to flesh out the concepts of the text. I also lent it to a co-worker for self-study in SVD for use in a graphics software program, and he commented that the book is very good for self-study. Overall, I would rate this as the most clear graduate textbook that I have used.

⭐the book is very lightly used by someone. some equations are marked with pencil, so I can easily erase the marks. there are some notes on the last a few chapters.

⭐This is an excellent text. I was fortunate enough to have Prof. Sadun teach a course from this book during my undergraduate career, and I still often reference the methods developed in this text in my graduate work. The book is written extremely clearly and provides excellent problems and examples for students. My fellow graduate students would ask to borrow this book when we would work on our quantum homeworks; the methods developed herein are just significantly more elegant than what they had learned elsewhere.I was just finally reminded to write this review because I don’t have the book with me right now and could really use it.

⭐exactly as I expected. fran-ds

⭐Very good book, fantastic analysis of the subject.

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